1. Find the derivative of function f '1, the inverse of function f, at the specied point a: = p. a) f(:(:) =4:c5+3:c3 andp = 7; b) f(:l:) = 1+w+sinm andp = l; c) f(9:) = 3/9? 4 andp = {75. 2. In this problem we discuss some functions that have historical names. 4 . . . . . a) The graph of y = $2 : 1 1s called the Newton's serpentme. Fll'ld the equations of the tangent km: to this graph at the origin and at the point (1, 2). 8 b) The graph of y = $2 + 4 is called the witch of Maria. Agnesi. Find the equation of the normal line to this graph at the point (2,1). c) The graph of y = % is called a catenary or a chain line. Let R be a point on this curve and let m-coordinate of R be r (r 7': 0). The tangent line to the curve at R crosses the m-axis at point Q. If P is the point ('r, 0), nd the length of PQ as a function of r and the limiting value of this length as 7' increases without bound. 3. Consider the curve my2 5633; = 6. vii; a) Find the expression for $ in terms of w and y (follow the example we discussed on the lecture). b) Find all points on the curve Whose sir-coordinate is 1, and write an equation for the tangent line at each of these points. c) Find the sis-coordinate of each point on the curve where the normal line is horizontal. 4 (ICEF Exam). Consider the function J(2) = arcsin (cos (sin (2) ) ) , 0